This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060552 #17 Dec 24 2024 13:45:56
%S A060552 0,0,0,1,2,7,14,35,70,154,310,650,1300,2666,5332,10788,21588,43428,
%T A060552 86856,174244,348488,697992,1396040,2794120,5588240,11180680,22361360,
%U A060552 44730896,89462032,178940432,357880864,715794960
%N A060552 a(n) is the number of distinct (modulo geometric D3-operations) nonsymmetric (no reflective nor rotational symmetry) patterns which can be formed by an equilateral triangular arrangement of closely packed black and white cells satisfying the local matching rule of Pascal's triangle modulo 2, where n is the number of cells in each edge of the arrangement. The matching rule is such that any elementary top-down triangle of three neighboring cells in the arrangement contains either one or three white cells.
%H A060552 Harry J. Smith, <a href="/A060552/b060552.txt">Table of n, a(n) for n=1..500</a>
%H A060552 A. Barbé, <a href="http://dx.doi.org/10.1016/S0166-218X(00)00211-0">Symmetric patterns in the cellular automaton that generates Pascal's triangle modulo 2</a>, Discr. Appl. Math. 105(2000), 1-38.
%H A060552 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A060552 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-4,-4,10,-4,-4,4,8,8,-16).
%F A060552 a(n) = (2^(n-1) - 2^(floor(n/3) + (n mod 3)mod 2 - 1))/3 + 2^(floor((n+3)/6) + d(n) - 1) - 2^floor((n-1)/2), with d(n)=1 if n mod 6=1 else d(n)=0.
%F A060552 a(n) = (A000079(n-1) - A060547(n)/2)/3 + A060548(n)/2 -A060546(n)/2.
%F A060552 a(n) = (A000079(n-1) - 2^(A008611(n-1) - 1))/3 + 2^(A008615(n+1) - 1) - 2^(A008619(n-1) - 1), n >= 1.
%F A060552 From _R. J. Mathar_, Aug 03 2009: (Start)
%F A060552 a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - 4*a(n-4) - 4*a(n-5) + 10*a(n-6) - 4*a(n-7) - 4*a(n-8) + 4*a(n-9) + 8*a(n-10) + 8*a(n-11) - 16*a(n-12).
%F A060552 G.f.: -x^4*(-1 - x^2 - x^4 + 2*x^3 + 2*x^5 + 2*x^6)/((2*x-1)*(2*x^2-1)*(2*x^3-1)*(2*x^6-1)). (End)
%o A060552 (PARI) a(n) = { (2^(n-1)-2^(floor(n/3)+(n%3)%2-1))/3+2^(floor((n+3)/6)+(n%6==1)-1)-2^floor((n-1)/2) } \\ _Harry J. Smith_, Jul 07 2009
%Y A060552 Cf. A000079, A060547, A060548, A060546, A060552, A008611, A008615, A008619.
%K A060552 easy,nonn
%O A060552 1,5
%A A060552 André Barbé (Andre.Barbe(AT)esat.kuleuven.ac.be), Apr 03 2001